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//
// GEANT4 Class header file
//
//
// File name:     G4AtimaEnergyLossModel
//
// Author:        Jose Luis Rodriguez Sanchez on base of ATIMA code
//
// Creation date: 16.01.2018
//
// Modifications:
// 09/10/2018: Solved bug in the determination of the material atomic number
//
// Class Description:
//
// This model calculates the stopping power of ions according 
// to the ATIMA code developed at GSI, Darmstadt, Germany.
// For details: http://web-docs.gsi.de/~weick/atima/
//
// Helmut Weick, GSI (responsible for fortran version)
// Andrej Prochazka, GSI (responsible for C version)
// Christoph Scheidenberger, GSI (project coordination)
//
// -------------------------------------------------------------------
//
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

#include "G4AtimaEnergyLossModel.hh"
#include "Randomize.hh"
#include "G4PhysicalConstants.hh"
#include "G4SystemOfUnits.hh"
#include "G4Electron.hh"
#include "G4GenericIon.hh"
#include "G4LossTableManager.hh"
#include "G4EmCorrections.hh"
#include "G4ParticleChangeForLoss.hh"
#include "G4DeltaAngle.hh"
#include "G4Log.hh"
#include "G4Exp.hh"
#include "G4Pow.hh"

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

using namespace std;

G4double G4AtimaEnergyLossModel::stepE = 0.0;
G4double G4AtimaEnergyLossModel::tableE[] = {0.0};

G4AtimaEnergyLossModel::G4AtimaEnergyLossModel(const G4ParticleDefinition*, 
                                     const G4String& nam)
  : G4VEmModel(nam),
    particle(nullptr),
    tlimit(DBL_MAX),
    isIon(false)
{
  g4calc = G4Pow::GetInstance();
  fParticleChange = nullptr;
  theElectron = G4Electron::Electron();
  SetParticle(theElectron);
  corr = G4LossTableManager::Instance()->EmCorrections();  
  nist = G4NistManager::Instance();
  SetLowEnergyLimit(2.0*MeV);
  MLN10 = 2.30258509299;
  atomic_mass_unit = 931.4940954; // MeV/c^2
  dedx_constant = 0.3070749187;  //4*pi*Na*me*c^2*r_e^2  //MeV cm^2
  electron_mass = 0.510998928;   // MeV/c^2
  fine_structure = 1.0/137.035999139;
  domega2dx_constant = dedx_constant*electron_mass;  //4*pi*Na*me*c^2*r_e^2  //MeV^2 cm^2
  if(tableE[0] == 0.0) {
    G4double logmin = 0.;
    G4double logmax = 5.;
    stepE = (logmax-logmin)/199.;
    for(G4int i=0; i<200; ++i){
      tableE[i] = G4Exp(MLN10*(logmin + ((G4double)i)*stepE));
    }
  }
}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

G4AtimaEnergyLossModel::~G4AtimaEnergyLossModel()
{}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

void G4AtimaEnergyLossModel::Initialise(const G4ParticleDefinition* p,
                                   const G4DataVector&)
{
  SetGenericIon(p);
  SetParticle(p);

  //G4cout << "G4AtimaEnergyLossModel::Initialise for " << p->GetParticleName()
  //         << "  isIon= " << isIon
  //         << G4endl;

  // always false before the run
  SetDeexcitationFlag(false);

  if(nullptr == fParticleChange) {
    fParticleChange = GetParticleChangeForLoss();
    if(UseAngularGeneratorFlag() && !GetAngularDistribution()) {
      SetAngularDistribution(new G4DeltaAngle());
    }
  }
}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

G4double G4AtimaEnergyLossModel::GetChargeSquareRatio(const G4ParticleDefinition* p,
                                                 const G4Material* mat,
                                                 G4double kineticEnergy)
{
  // this method is called only for ions
  G4double q2 = corr->EffectiveChargeSquareRatio(p,mat,kineticEnergy);
  corrFactor = q2*corr->EffectiveChargeCorrection(p,mat,kineticEnergy);
  return corrFactor;
}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

G4double G4AtimaEnergyLossModel::GetParticleCharge(const G4ParticleDefinition* p,
                                              const G4Material* mat,
                                              G4double kineticEnergy)
{
  //G4cout<<"G4AtimaEnergyLossModel::GetParticleCharge e= "<<kineticEnergy <<
  //  " q= " <<  corr->GetParticleCharge(p,mat,kineticEnergy) <<G4endl;
  // this method is called only for ions, so no check if it is an ion
  return corr->GetParticleCharge(p,mat,kineticEnergy);
}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....

void G4AtimaEnergyLossModel::SetupParameters()
{
  mass = particle->GetPDGMass();
  spin = particle->GetPDGSpin();
  G4double q = particle->GetPDGCharge()/eplus;
  chargeSquare = q*q;
  corrFactor = chargeSquare;
  ratio = electron_mass_c2/mass;
  static const G4double aMag = 1./(0.5*eplus*hbar_Planck*c_squared);
  G4double magmom = particle->GetPDGMagneticMoment()*mass*aMag;
  magMoment2 = magmom*magmom - 1.0;
  formfact = 0.0;
  tlimit = DBL_MAX;
  if(particle->GetLeptonNumber() == 0) {
    G4int iz = G4lrint(q);
    if(iz <= 1) {
      formfact = (spin == 0.0 && mass < GeV) ? 1.181e-6 : 1.548e-6;	
    } else {
      G4double x = nist->GetA27(iz);
      formfact = 3.969e-6*x*x;
    }
    tlimit = std::sqrt(0.414/formfact +
                       electron_mass_c2*electron_mass_c2) - electron_mass_c2;
  }
}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

G4double G4AtimaEnergyLossModel::MinEnergyCut(const G4ParticleDefinition*,
                                         const G4MaterialCutsCouple* couple)
{
  return couple->GetMaterial()->GetIonisation()->GetMeanExcitationEnergy();
}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

G4double 
G4AtimaEnergyLossModel::ComputeCrossSectionPerElectron(const G4ParticleDefinition* p,
                                                  G4double kineticEnergy,
                                                  G4double cutEnergy,
                                                  G4double maxKinEnergy)        
{
  G4double cross = 0.0;
  G4double tmax = MaxSecondaryEnergy(p, kineticEnergy);
  G4double maxEnergy = std::min(tmax,maxKinEnergy);
  if(cutEnergy < maxEnergy) {

    G4double totEnergy = kineticEnergy + mass;
    G4double energy2   = totEnergy*totEnergy;
    G4double beta2     = kineticEnergy*(kineticEnergy + 2.0*mass)/energy2;

    cross = (maxEnergy - cutEnergy)/(cutEnergy*maxEnergy) 
      - beta2*G4Log(maxEnergy/cutEnergy)/tmax;

    // +term for spin=1/2 particle
    if( 0.0 < spin ) { cross += 0.5*(maxEnergy - cutEnergy)/energy2; }

    cross *= twopi_mc2_rcl2*chargeSquare/beta2;
  }
  
   // G4cout << "BB: e= " << kineticEnergy << " tmin= " << cutEnergy 
   //        << " tmax= " << tmax << " cross= " << cross << G4endl;
  
  return cross;
}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

G4double G4AtimaEnergyLossModel::ComputeCrossSectionPerAtom(
                                           const G4ParticleDefinition* p,
                                                 G4double kineticEnergy,
                                                 G4double Z, G4double,
                                                 G4double cutEnergy,
                                                 G4double maxEnergy)
{
  G4double cross = Z*ComputeCrossSectionPerElectron
                                         (p,kineticEnergy,cutEnergy,maxEnergy);
  return cross;
}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

G4double G4AtimaEnergyLossModel::CrossSectionPerVolume(
                                           const G4Material* material,
                                           const G4ParticleDefinition* p,
                                                 G4double kineticEnergy,
                                                 G4double cutEnergy,
                                                 G4double maxEnergy)
{
  G4double eDensity = material->GetElectronDensity();
  G4double cross = eDensity*ComputeCrossSectionPerElectron
                                         (p,kineticEnergy,cutEnergy,maxEnergy);
  return cross;
}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

G4double G4AtimaEnergyLossModel::ComputeDEDXPerVolume(const G4Material* material,
                                                 const G4ParticleDefinition* p,
                                                 G4double kineticEnergy,
                                                 G4double)
{
  //Call to ATIMA Stopping Power function
  G4double zt = material->GetIonisation()->GetZeffective();
  zt = std::min(zt,93.); 
  G4double at = nist->GetAtomicMassAmu(G4lrint(zt));
  G4double dedx = StoppingPower(p->GetPDGMass(), p->GetPDGCharge(), 
    kineticEnergy/(MeV), at, zt) *material->GetDensity()/(g/cm3);
  dedx = std::max(dedx, 0.0);

  //  G4cout << "E(MeV)= " << kineticEnergy/MeV << " dedx= " << dedx 
  //          << "  " << material->GetName() << G4endl;
  return dedx;
}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

void G4AtimaEnergyLossModel::CorrectionsAlongStep(const G4MaterialCutsCouple* couple,
                                             const G4DynamicParticle* dp,
                                             G4double& eloss,
                                             G4double&,
                                             G4double length)
{
  if(isIon) {
    const G4ParticleDefinition* p = dp->GetDefinition();
    const G4Material* mat = couple->GetMaterial();
    G4double cutEnergy = DBL_MAX;
    GetModelOfFluctuations()->SetParticleAndCharge(p, p->GetPDGCharge());
    G4double kineticEnergy = dp->GetKineticEnergy();
    eloss = ComputeDEDXPerVolume(mat, p, kineticEnergy, cutEnergy)*length/(cm);   
  }

}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

void G4AtimaEnergyLossModel::SampleSecondaries(vector<G4DynamicParticle*>* vdp,
                                          const G4MaterialCutsCouple* couple,
                                          const G4DynamicParticle* dp,
                                          G4double minKinEnergy,
                                          G4double maxEnergy)
{
  G4double kineticEnergy = dp->GetKineticEnergy();
  G4double tmax = MaxSecondaryEnergy(dp->GetDefinition(),kineticEnergy);

  G4double maxKinEnergy = std::min(maxEnergy,tmax);
  if(minKinEnergy >= maxKinEnergy) { return; }

  //G4cout << "G4AtimaEnergyLossModel::SampleSecondaries Emin= " << minKinEnergy
  //         << " Emax= " << maxKinEnergy << G4endl;

  G4double totEnergy     = kineticEnergy + mass;
  G4double etot2         = totEnergy*totEnergy;
  G4double beta2         = kineticEnergy*(kineticEnergy + 2.0*mass)/etot2;

  G4double deltaKinEnergy, f; 
  G4double f1 = 0.0;
  G4double fmax = 1.0;
  if( 0.0 < spin ) { fmax += 0.5*maxKinEnergy*maxKinEnergy/etot2; }

  CLHEP::HepRandomEngine* rndmEngineMod = G4Random::getTheEngine();
  G4double rndm[2];

  // sampling without nuclear size effect
  do {
    rndmEngineMod->flatArray(2, rndm);
    deltaKinEnergy = minKinEnergy*maxKinEnergy
                    /(minKinEnergy*(1.0 - rndm[0]) + maxKinEnergy*rndm[0]);

    f = 1.0 - beta2*deltaKinEnergy/tmax;
    if( 0.0 < spin ) {
      f1 = 0.5*deltaKinEnergy*deltaKinEnergy/etot2;
      f += f1;
    }

    // Loop checking, 03-Aug-2015, Vladimir Ivanchenko
  } while( fmax*rndm[1] > f);

  // projectile formfactor - suppresion of high energy
  // delta-electron production at high energy
  
  G4double x = formfact*deltaKinEnergy*(deltaKinEnergy + 2*electron_mass_c2);
  if(x > 1.e-6) {

    G4double x10 = 1.0 + x;
    G4double grej  = 1.0/(x10*x10);
    if( 0.0 < spin ) {
      G4double x2 = 0.5*electron_mass_c2*deltaKinEnergy/(mass*mass);
      grej *= (1.0 + magMoment2*(x2 - f1/f)/(1.0 + x2));
    }
    if(grej > 1.1) {
      G4cout << "### G4AtimaEnergyLossModel WARNING: grej= " << grej
             << "  " << dp->GetDefinition()->GetParticleName()
             << " Ekin(MeV)= " <<  kineticEnergy
             << " delEkin(MeV)= " << deltaKinEnergy
             << G4endl;
    }
    if(rndmEngineMod->flat() > grej) { return; }
  }

  G4ThreeVector deltaDirection;

  if(UseAngularGeneratorFlag()) {

    const G4Material* mat =  couple->GetMaterial();
    G4int Z = SelectRandomAtomNumber(mat);

    deltaDirection = 
      GetAngularDistribution()->SampleDirection(dp, deltaKinEnergy, Z, mat);

  } else {
 
    G4double deltaMomentum =
      std::sqrt(deltaKinEnergy * (deltaKinEnergy + 2.0*electron_mass_c2));
    G4double cost = deltaKinEnergy * (totEnergy + electron_mass_c2) /
      (deltaMomentum * dp->GetTotalMomentum());
    if(cost > 1.0) { cost = 1.0; }
    G4double sint = std::sqrt((1.0 - cost)*(1.0 + cost));

    G4double phi = twopi*rndmEngineMod->flat();

    deltaDirection.set(sint*cos(phi),sint*sin(phi), cost) ;
    deltaDirection.rotateUz(dp->GetMomentumDirection());
  }  
  /*
    G4cout << "### G4AtimaEnergyLossModel " 
           << dp->GetDefinition()->GetParticleName()
           << " Ekin(MeV)= " <<  kineticEnergy
           << " delEkin(MeV)= " << deltaKinEnergy
           << " tmin(MeV)= " << minKinEnergy
           << " tmax(MeV)= " << maxKinEnergy
           << " dir= " << dp->GetMomentumDirection()
           << " dirDelta= " << deltaDirection
           << G4endl;
  */
  // create G4DynamicParticle object for delta ray
  G4DynamicParticle* delta = 
    new G4DynamicParticle(theElectron,deltaDirection,deltaKinEnergy);

  vdp->push_back(delta);

  // Change kinematics of primary particle
  kineticEnergy -= deltaKinEnergy;
  G4ThreeVector finalP = dp->GetMomentum() - delta->GetMomentum();
  finalP               = finalP.unit();
  
  fParticleChange->SetProposedKineticEnergy(kineticEnergy);
  fParticleChange->SetProposedMomentumDirection(finalP);
}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....

G4double G4AtimaEnergyLossModel::MaxSecondaryEnergy(const G4ParticleDefinition* pd,
                                               G4double kinEnergy) 
{
  // here particle type is checked for any method
  SetParticle(pd);
  G4double tau  = kinEnergy/mass;
  G4double tmax = 2.0*electron_mass_c2*tau*(tau + 2.) /
                  (1. + 2.0*(tau + 1.)*ratio + ratio*ratio);
  return std::min(tmax,tlimit);
}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

G4double G4AtimaEnergyLossModel::StoppingPower(G4double ap, G4double zp, 
         G4double ep, G4double at, G4double zt){
  //
  if(ep==0)return 0.0;
  ap=ap/atomic_mass_unit;
  ep=ep/ap;
  G4double se = 0.0;
  // ep in MeV
  if(ep<=10.){
        se = sezi_dedx_e(zp, ep, at, zt);
  }
  else if(ep>10. && ep<30.){
    G4double factor = 0.05 * ( ep - 10.0 );
    se = (1.0-factor)*sezi_dedx_e(zp, ep, at, zt) + factor*Bethek_dedx_e(ap, zp, ep, at, zt);
  }
  else {
    se = Bethek_dedx_e(ap, zp, ep, at, zt);
  }
  return se + dedx_n(ap, zp, ep, at, zt);
}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

G4double G4AtimaEnergyLossModel::dedx_n(const G4double ap, const G4double zp, 
         const G4double ep, const G4double at, const G4double zt){
    
  G4double zpowers = g4calc->powA(zp,0.23)+g4calc->powA(zt,0.23);
  G4double asum = ap + at;
  G4double epsilon = 32.53*at*1000.*ep*ap/(zp*zt*asum*zpowers); //projectile energy is converted from MeV/u to keV
  G4double sn=0.;
    
  if(epsilon<=30.0){
    sn = G4Log(1.+(1.1383*epsilon))/ (2.*(epsilon + 0.01321*g4calc->powA(epsilon,0.21226) + 0.19593*sqrt(epsilon)));
  }
  else{
    sn = G4Log(epsilon)/(2.*epsilon);
  }
  sn = 100.*8.4621*zp*zt*ap*sn*Avogadro/1.e+23/(asum*zpowers*at);
  return sn;
}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

G4double G4AtimaEnergyLossModel::sezi_dedx_e(const G4double zp, const G4double ep, const G4double at, const G4double zt){
  G4double e = ep*1000.; // e in keV/u
  G4double se = 0.;

  // heavy ion Z > 2
  G4double h1,h4;
  G4double a,q,b;
  G4double l1,l0,l;
  G4double YRmin = 0.130; //  YRmin = VR / ZP**0.67 <= 0.13 OR VR <= 1.0
  G4double VRmin = 1.0;
  G4double vfermi = atima_vfermi[(G4int)zt-1];
  G4double yr=0;
  G4double zeta = 0;
        
  G4double v = std::sqrt(e/25.0)/vfermi;
  G4double v2= v*v;
        
  G4double vr = (v >= 1)? v*vfermi*(1.+ 1./(5.*v2)) : 3.0*vfermi/4.0*(1.0+v2*(2.0/3.0-v2/15.0));
        
  h1= 1./g4calc->powA(zp,0.6667);
  yr = std::max(YRmin,vr*h1);
  yr = std::max(yr, VRmin*h1);
        
  //--  CALCULATE ZEFF
  a = -0.803*g4calc->powA(yr,0.3) + 1.3167*g4calc->powA(yr,0.6) + 0.38157*yr + 0.008983*yr*yr;
  q = std::min(1.0, std::max(0.0 , (1.0 - G4Exp(-std::min(a, 50.0))))); //-- Q = IONIZATION LEVEL OF THE ION AT RELATIVE VELOCITY YR
        
  //-- IONIZATION LEVEL TO EFFECTIVE CHARGE
  h1 = 1./g4calc->powA(zp,0.3333);
        
  b = (std::min(0.43, std::max(0.32,0.12 + 0.025*zp)))*h1;
  l0 = (0.8 - q * std::min(1.2,0.6 +zp/30.0))*h1;
        if(q < 0.2){
            l1 = 0;
            }
        else{
            if (q < std::max(0.0,0.9-0.025*zp)){
                l1 = b*(q-0.2)/std::abs(std::max(0.0,0.9-0.025*zp)-0.2000001);
                }
	     	 else{
             	if(q < std::max(0.0,1.0 - 0.025*std::min(16.,zp))) l1 = b;
                else l1 = b*(1.0 - q)/(0.025*std::min(16.,zp));
                }
        }
        // calculate screening
        l = std::max(l1,l0*atima_lambda_screening[(G4int)zp-1]);
        h1 =4.0*l*vfermi/1.919;
        zeta = q + (1./(2.*(vfermi*vfermi)))*(1. - q)* G4Log(1. + h1*h1);
         
         // ZP**3 EFFECT AS IN REF. 779?
        a = 7.6 - std::max(0.0, G4Log(e));
        zeta = zeta*(1. + (1./(zp*zp))*(0.18 + .0015*zt)*G4Exp(-a*a));
        
        h1= 1./g4calc->powA(zp,0.6667);
        if (yr <= ( std::max(YRmin, VRmin*h1))){
            VRmin=std::max(VRmin, YRmin/h1);
            //--C        ..CALCULATE VELOCITY STOPPING FOR YR < YRmin
            G4double vmin =.5*(VRmin + std::sqrt(std::max(0.0,VRmin*VRmin - 0.8*vfermi*vfermi)));
            G4double eee = 25.0*vmin*vmin;
            G4double eval = 1.0;
            if((zt == 6) || (((zt == 14) || (zt == 32)) &&  (zp <= 19))) eval = 0.35;
            else eval = 0.5;
            
            h1 = zeta *zp;
            h4 = g4calc->powA(e / eee,eval);
            se = sezi_p_se(eee*0.001,at,zt) * h1*h1*h4;
            return se;
        }
        else {
            se = sezi_p_se(ep,at,zt)*g4calc->powA(zeta*zp,2.0);
            return se;
        }

   return se;
}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

G4double G4AtimaEnergyLossModel::sezi_p_se(const G4double energy, const G4double at, const G4double zt){
  G4double sp = 0.;
  G4double e = 1000*energy; //e in keV/u
  G4int i = zt - 1;
    
  if(e<=25)e=25;
   G4double sl = (proton_stopping_coef[i][0]*g4calc->powA(e,proton_stopping_coef[i][1])) + (proton_stopping_coef[i][2]*g4calc->powA(e,proton_stopping_coef[i][3]));
   G4double sh = proton_stopping_coef[i][4]/g4calc->powA(e,proton_stopping_coef[i][5]) * G4Log( (proton_stopping_coef[i][6]/e) + (proton_stopping_coef[i][7]*e));
   sp = sl*sh/(sl+sh);
   e=1000*energy;
   if(e<=25){
       sp *=(zt>6)?g4calc->powA(e/25.,0.45):g4calc->powA(e/25.,0.25);
   }
  return 100.*sp*Avogadro/1.e+23/at;
}


//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

G4double G4AtimaEnergyLossModel::Bethek_dedx_e(G4double ap, G4double zp, G4double ep, G4double at, G4double zt){
//
// According to C. Scheidenberger et al., Phys. Rev. Lett. 73, 50 (1994).
//
    G4double gamma=1.0 + ep/atomic_mass_unit;
    G4double beta2=1.0-1.0/(gamma*gamma);
    //
    G4double beta = std::sqrt(beta2);
    G4double zp_eff = zp*(1.0-G4Exp(-0.95/fine_structure*beta/g4calc->A23(zp)));
    G4int zi = std::min(std::max((G4int)zt, 1), 120);
    G4double Ipot = ionisation_potentials_z[zi];
    G4double f1 = dedx_constant*g4calc->powA(zp_eff,2.)*zt/(beta2*at);

    //
    G4double f2 = G4Log(2.0*electron_mass*1000000*beta2/Ipot);
    G4double eta = beta*gamma;

    if(!(eta>=0.13)){ //shell corrections
        G4double cor = (+0.422377*g4calc->powA(eta,-2.)
                    +0.0304043*g4calc->powA(eta,-4.)
                    -0.00038106*g4calc->powA(eta,-6.))*1e-6*g4calc->powA(Ipot,2.) 
                  +(+3.858019*g4calc->powA(eta,-2.) 
                    -0.1667989*(g4calc->powA(eta,-4.))
                    +0.00157955*(g4calc->powA(eta,-6.)))*1.0e-9*g4calc->powA(Ipot,3.); 
        f2 = f2 -cor/zt;
    }

    f2+=2*G4Log(gamma) -beta2;

    //Barkas correction
    G4double barkas=1.0;
    G4double V2FVA[4]={0.33,0.30,0.26,0.23};
    G4double VA[4]={1.,2.,3.,4.};
    G4double v1 = eta/(fine_structure*std::sqrt(zt));
    G4double v2fv;
    if(v1 >= 4.){
        v2fv = 0.45 / std::sqrt(v1);
        }
    else if(v1 > 1. && v1 < 4.){//VALUES FROM THE JACKSON MC CARTHY FUNCTION //PHYS. REV. B 6 4131
        G4int i=1;
        for(; i<4; i++){
	  if(VA[i] >= v1) break;
	}
        i = std::min(i, 3);
	v2fv = V2FVA[i-1]+(v1-VA[i-1])*(V2FVA[i]-V2FVA[i-1])/(VA[i]-VA[i-1]);
    }
    else{
        v2fv=0;
    }
    barkas= 1.0+2.0 * zp_eff * v2fv /(v1*v1*std::sqrt(zt));

    //Fermi-density effect for relativistic velocities
    gamma = 1./std::sqrt(1-(beta*beta));
    G4double x = G4Log(beta * gamma) / 2.302585;
    G4int i = std::min(std::max(zi-1,0), 91);
    G4double del = 0.;
    
    if (x < x0[i] ){
        if(del_0[i] > 0.)del = del_0[i] * g4calc->powA(10.0,(2.*(x-x0[i])));
        }
    else {
        del = 4.6052 * x - c[i];
        if ( x0[i]<= x &&  x <= x1[i] ) del +=  afermi[i] * g4calc->powA((x1[i] - x),m0[i]);
        }

    //Precalculated lindhard correction
    G4double LS = 0.;
    G4int z = G4lrint(zp);
    if(z>109)z=109;
    if(ep<tableE[0])ep=tableE[0];

    G4double da = (ap - element_atomic_weights[z])/element_atomic_weights[z];
    z = z-1;

    G4double v3 = EnergyTable_interpolate(ep,ls_coefficients_a[z]);
    G4double v4 = EnergyTable_interpolate(ep,ls_coefficients_ahi[z]);
    G4double dif = v4 - v3;
    LS = v3+(dif*da/0.05);

    //Final stopping power
    G4double result  = (f2)*barkas + LS - del/2.;
    result *=f1;
    
    return result;
}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

G4double G4AtimaEnergyLossModel::EnergyTable_interpolate(G4double xval,const G4double* y){
     G4double r;
     G4int num=200;
     G4double lxval = G4Log(xval)/MLN10;
     if(xval<tableE[0] || xval>tableE[num-1])return 0.0;
     if(xval==tableE[num-1])return y[num-1];
     G4int i = (G4int)(lxval/stepE);
     i = std::min(std::max(i, 0), num-2);
     G4double linstep = tableE[i+1] - tableE[i];
     G4double x = 1.0 - ((xval - tableE[i])/linstep);
     r = (x*y[i]) + ((1-x)*y[i+1]);
     return r;
}

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

const G4double G4AtimaEnergyLossModel::proton_stopping_coef[92][8] = { // proton in material stopping coefficient
{  .0091827, .0053496, .69741, .48493, 316.07,1.0143, 9329.3, .0539890}, //H
{  .11393, .0051984, 1.0822, .39252,  1081.0, 1.0645, 4068.5, .0176990}, //He
{  .85837, .0050147, 1.6044, .38844,  1337.3, 1.0470, 2659.2, .01898},
{  .8781,  .0051049, 5.4232, .2032,   1200.6, 1.0211, 1401.8, .0385290},
{ 1.4608,  .0048836, 2.338,  .44249, 1801.3, 1.0352, 1784.1, .02024},
{ 3.2579,  .0049148, 2.7156, .36473, 2092.2, 1.0291, 2643.6, .0182370}, //C
{  .59674, .0050837, 4.2073, .30612,  2394.2, 1.0255, 4892.1, .0160060},
{  .75253, .0050314, 4.0824, .30067, 2455.8, 1.0181, 5069.7, .0174260}, //O
{ 1.226,   .0051385, 3.2246, .32703, 2525.0, 1.0142, 7563.6, .0194690},
{ 1.0332,  .0051645, 3.004,  .33889, 2338.6, .99997, 6991.2, .0217990}, //Ne
{ 6.0972,  .0044292, 3.1929, .45763, 1363.3, .95182, 2380.6, .0818350},
{14.013,   .0043646, 2.2641, .36326, 2187.4, .99098, 6264.8, .0462},
{ .039001, .0045415, 5.5463, .39562, 1589.2, .95316, 816.16, .0474840},
{ 2.072,   .0044516, 3.5585, .53933, 1515.2, .93161, 1790.3, .0351980},
{17.575,   .0038346, .078694, 1.2388,2806.0, .97284, 1037.6, .0128790},
{16.126,   .0038315, .054164, 1.3104,2813.3, .96587, 1251.4, .0118470},
{ 3.217,   .0044579, 3.6696, .5091,  2734.6, .96253, 2187.5, .0169070},
{ 2.0379,  .0044775, 3.0743, .54773, 3505.0, .97575, 1714.00, .0117010},
{ .74171, .0043051, 1.1515, .95083,   917.21, .8782, 389.93, .18926},
{ 9.1316,  .0043809, 5.4611, .31327, 3891.8, .97933, 6267.9, .0151960}, //Ca
{ 7.2247,  .0043718, 6.1017, .37511, 2829.2, .95218, 6376.1, .0203980},
{  .147,   .0048456, 6.3485, .41057, 2164.1, .94028, 5292.6, .0502630},
{ 5.0611,  .0039867, 2.6174, .57957, 2218.9, .92361, 6323.00, .0256690},
{  .53267, .0042968, .39005, 1.2725, 1872.7, .90776, 64.166, .0301070},
{  .47697, .0043038, .31452, 1.3289, 1920.5, .90649, 45.576, .0274690},
{  .027426, .0035443, .031563, 2.1755,  1919.5, .90099, 23.902, .0253630},
{  .16383, .0043042, .073454, 1.8592, 1918.4, .89678, 27.61, .0231840},
{ 4.2562,  .0043737, 1.5606, .72067, 1546.8, .87958, 302.02, .0409440}, //Ni
{ 2.3508,  .0043237, 2.882,  .50113, 1837.7, .89992, 2377.00, .04965},
{ 3.1095,  .0038455, .11477, 1.5037, 2184.7, .89309, 67.306, .0165880},
{15.322,   .0040306, .65391, .67668, 3001.7, .92484, 3344.2, .0163660},
{ 3.6932,  .0044813, 8.608,  .27638,  2982.7, .9276, 3166.6, .0308740},
{ 7.1373,  .0043134, 9.4247, .27937,  2725.8, .91597, 3166.1, .0250080},
{ 4.8979,  .0042937, 3.7793, .50004,  2824.5, .91028, 1282.4, .0170610},
{ 1.3683,  .0043024, 2.5679, .60822,  6907.8, .9817, 628.01, .0068055},
{ 1.8301,  .0042983, 2.9057, .6038,   4744.6, .94722, 936.64, .0092242},
{  .42056, .0041169, .01695, 2.3616, 2252.7, .89192, 39.752, .0277570},
{30.78,    .0037736, .55813, .76816, 7113.2, .97697, 1604.4, .0065268},
{11.576,   .0042119, 7.0244, .37764, 4713.5, .94264, 2493.2, .01127},
{ 6.2406,  .0041916, 5.2701, .49453, 4234.6, .93232, 2063.9, .0118440},
{  .33073, .0041243, 1.7246, 1.1062, 1930.2, .86907, 27.416, .0382080},
{  .017747, .0041715, .14586, 1.7305,1803.6, .86315, 29.669, .0321230},
{ 3.7229,  .0041768, 4.6286, .56769, 1678.0, .86202, 3094.00, .06244},
{  .13998, .0041329, .25573, 1.4241, 1919.3, .86326, 72.797, .0322350},
{  .2859,  .0041386, .31301, 1.3424, 1954.8, .86175, 115.18, .0293420},
{ .76,    .0042179, 3.386,  .76285,  1867.4, .85805, 69.994, .0364480},
{ 6.3957,  .0041935, 5.4689, .41378, 1712.6, .85397,18493.00, .0564710},
{ 3.4717,  .0041344, 3.2337, .63788, 1116.4, .81959, 4766.0, .1179},
{ 2.5265,  .0042282, 4.532,  .53562, 1030.8, .81652,16252.0, .19722},
{ 7.3683,  .0041007, 4.6791, .51428, 1160.0, .82454,17965.0, .13316},
{ 7.7197,  .004388, 3.242,   .68434, 1428.1, .83398, 1786.7, .0665120},
{16.78,    .0041918, 9.3198, .29568, 3370.9, .90289, 7431.7, .02616},
{ 4.2132,  .0042098, 4.6753, .57945, 3503.9, .89261, 1468.9, .0143590},
{ 4.0818,  .004214, 4.4425,  .58393, 3945.3, .90281, 1340.5, .0134140}, //Xe
{.18517, .0036215, .00058788,3.5315, 2931.3, .88936, 26.18, .0263930},
{ 4.8248,  .0041458, 6.0934, .57026, 2300.1, .86359, 2980.7, .0386790},
{  .49857, .0041054, 1.9775, .95877, 786.55, .78509, 806.6, .40882},
{ 3.2754,  .0042177, 5.768,  .54054, 6631.3, .94282, 744.07, .0083026},
{ 2.9978,  .0040901, 4.5299, .62025, 2161.2, .85669, 1268.6, .0430310},
{ 2.8701,  .004096, 4.2568,  .6138,  2130.4, .85235, 1704.1, .0393850},
{10.853,   .0041149, 5.8907, .46834, 2857.2, .8755, 3654.2, .0299550},
{ 3.6407,  .0041782, 4.8742, .57861, 1267.7, .82211, 3508.2, .24174},
{17.645,   .0040992, 6.5855, .32734, 3931.3, .90754, 5156.7, .0362780},
{ 7.5309,  .0040814, 4.9389, .50679, 2519.7, .85819, 3314.6, .0305140},
{ 5.4742,  .0040829, 4.897,  .51113, 2340.1, .85296, 2342.7, .0356620},
{ 4.2661,  .0040667, 4.5032, .55257, 2076.4, .84151, 1666.6, .0408010},
{ 6.8313,  .0040486, 4.3987, .51675, 2003.0, .83437, 1410.4, .03478},
{ 1.2707,  .0040553, 4.6295, .57428, 1626.3, .81858, 995.68, .0553190},
{ 5.7561,  .0040491, 4.357,  .52496, 2207.3, .83796, 1579.5, .0271650},
{14.127,   .0040596, 5.8304, .37755, 3645.9, .87823, 3411.8, .0163920},
{ 6.6948,  .0040603, 4.9361, .47961, 2719.0, .85249, 1885.8, .0197130},
{ 3.0619,  .0040511, 3.5803, .59082, 2346.1, .83713, 1222.0, .0200720},
{10.811,   .0033008, 1.3767, .76512, 2003.7, .82269, 1110.6, .0249580},
{ 2.7101,  .0040961, 1.2289, .98598, 1232.4, .79066, 155.42, .0472940},
{  .52345, .0040244, 1.4038, .8551,  1461.4, .79677, 503.34, .0367890},
{  .4616,  .0040203, 1.3014, .87043, 1473.5, .79687, 443.09, .0363010},
{  .97814, .0040374, 2.0127, .7225,  1890.8, .81747, 930.7, .02769},
{ 3.2086,  .004051, 3.6658,  .53618, 3091.2, .85602, 1508.1, .0154010},
{ 2.0035,  .0040431, 7.4882, .3561,  4464.3, .88836, 3966.5, .0128390},
{15.43,    .0039432, 1.1237, .70703, 4595.7, .88437, 1576.5, .0088534},
{ 3.1512,  .0040524, 4.0996, .5425,  3246.3, .85772, 1691.8, .0150580},
{ 7.1896,  .0040588, 8.6927, .35842, 4760.6, .88833, 2888.3, .0110290}, //Pb
{ 9.3209,  .004054, 11.543,  .32027, 4866.2, .89124, 3213.4, .0119350},
{29.242,   .0036195, .16864, 1.1226, 5688.0, .89812, 1033.3, .0071303},
{ 1.8522,  .0039973, 3.1556, .65096, 3755.0, .86383, 1602.0, .0120420},
{ 3.222,   .0040041, 5.9024, .52678, 4040.2, .86804, 1658.4, .0117470},
{ 9.3412,  .0039661, 7.921,  .42977, 5180.9, .88773, 2173.2, .0092007},
{36.183,   .0036003, .58341, .86747, 6990.2, .91082, 1417.1, .0062187},
{ 5.9284,  .0039695, 6.4082, .52122, 4619.5, .88083, 2323.5, .0116270},
{ 5.2454,  .0039744, 6.7969, .48542, 4586.3, .87794, 2481.5, .0112820},
{33.702,   .0036901, .47257, .89235, 5295.7, .8893, 2053.3, .0091908},
{2.7589,  .0039806, 3.2092, .66122,  2505.4, .82863, 2065.1, .0228160} //U
};

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

const G4double G4AtimaEnergyLossModel::atima_vfermi[92] = {
1.0309, 
0.15976,
0.59782,
1.0781, 
1.0486, 
1.00,   
1.058,  
0.93942,
0.74562,
0.3424, 
0.45259,
0.71074,
0.90519,
0.97411,
0.97184,
0.89852,
0.70827,
0.39816,
0.36552,
0.62712,
0.81707,
0.9943, 
1.1423, 
1.2381, 
1.1222, 
0.92705,
1.0047, 
1.2,    
1.0661, 
0.97411,
0.84912,
0.95,   
1.0903, 
1.0429, 
0.49715,
0.37755,
0.35211,
0.57801,
0.77773,
1.0207, 
1.029,  
1.2542, 
1.122,  
1.1241, 
1.0882, 
1.2709, 
1.2542, 
0.90094,
0.74093,
0.86054,
0.93155,
1.0047, 
0.55379,
0.43289,
0.32636,
0.5131, 
0.6950, 
0.72591,
0.71202,
0.67413,
0.71418,
0.71453,
0.5911, 
0.70263,
0.68049,
0.68203,
0.68121,
0.68532,
0.68715,
0.61884,
0.71801,
0.83048,
1.1222, 
1.2381, 
1.045,  
1.0733, 
1.0953, 
1.2381, 
1.2879, 
0.78654,
0.66401,
0.84912,
0.88433,
0.80746,
0.43357,
0.41923,
0.43638,
0.51464,
0.73087,
0.81065,
1.9578, 
1.0257
};

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

const G4double G4AtimaEnergyLossModel::atima_lambda_screening[92]= {
 1.00,
 1.00,
 1.10,
 1.06,
 1.01,
 1.03,
 1.04,
 0.99,
 0.95,
 0.90,
 0.82,
 0.81,
 0.83,
 0.88,
 1.00,
 0.95,
 0.97,
 0.99,
 0.98,
 0.97,
 0.98,
 0.97,
 0.96,
 0.93,
 0.91,
 0.9, 
 0.88,
 0.9, 
 0.9, 
 0.9, 
 0.9, 
 0.85,
 0.9, 
 0.9, 
 0.91,
 0.92,
 0.9, 
 0.9, 
 0.9, 
 0.9, 
 0.9, 
 0.88,
 0.9, 
 0.88,
 0.88,
 0.9, 
 0.9, 
 0.88,
 0.9, 
 0.9, 
 0.9, 
 0.9, 
 0.96,
 1.2, 
 0.9, 
 0.88,
 0.88,
 0.85,
 0.90,
 0.90,
 0.92,
 0.95,
 0.99,
 1.03,
 1.05,
 1.07,
 1.08,
 1.10,
 1.08,
 1.08,
 1.08,
 1.08,
 1.09,
 1.09,
 1.10,
 1.11,
 1.12,
 1.13,
 1.14,
 1.15,
 1.17,
 1.20,
 1.18,
 1.17,
 1.17,
 1.16,
 1.16,
 1.16,
 1.16,
 1.16,
 1.16,
 1.16
};

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

const G4double G4AtimaEnergyLossModel::element_atomic_weights[110]={
 0.0,
 1.00794, //H
 4.0026, //He
 6.941, //Li
 9.01218, //Be
 10.811, //B
 12.0107, //C
 14.0067, //N
 15.9994, //O
 18.9984, //F
 20.1797, //Ne
 22.9898, //Na
 24.305, //Mg
 26.9815, //Al
 28.0855, //Si
 30.9738, //P
 32.065, //S
 35.453, //Cl
 39.948, //Ar
 39.0983, //K
 40.078, //Ca
 44.9559, //Sc
 47.867, //Ti
 50.9415, //V
 51.9961, //Cr
 54.938, //Mn
 55.845, //Fe
 58.9332, //Co
 58.6934, //Ni
 63.546, //Cu
 65.409, //Zn
 69.723, //Ga
 72.64, //Ge
 74.9216, //As
 78.96, //Se
 79.904, //Br
 83.798, //Kr
 85.4678, //Rb
 87.62, //Sr
 88.9059, //Y
 91.224, //Zr
 92.9064, //Nb
 95.94, //Mo
 97.9072, //Tc
 101.07, //Ru
 102.906, //Rh
 106.42, //Pd
 107.868, //Ag
 112.411, //Cd
 114.818, //In
 118.71, //Sn
 121.76, //Sb
 127.6, //Te
 126.904, //I
 131.293, //Xe
 132.905, //Cs
 137.327, //Ba
 138.905, //La
 140.116, //Ce
 140.908, //Pr
 144.24, //Nd
 144.913, //Pm
 150.36, //Sm
 151.964, //Eu
 157.25, //Gd
 158.925, //Tb
 162.5, //Dy
 164.93, //Ho
 167.259, //Er
 168.934, //Tm
 173.04, //Yb
 174.967, //Lu
 178.49, //Hf
 180.948, //Ta
 183.84, //W
 186.207, //Re
 190.23, //Os
 192.217, //Ir
 195.078, //Pt
 196.967, //Au
 200.59, //Hg
 204.383, //Tl
 207.2, //Pb
 208.98, //Bi
 208.982, //Po
 209.987, //At
 222.018, //Rn
 223.02, //Fr
 226.025, //Ra
 227.028, //Ac
 232.038, //Th
 231.036, //Pa
 238.029, //U
 237.048, //Np
 244.064, //Pu
 243.061, //Am
 247.07, //Cm
 247.07, //Bk
 251.08, //Cf
 252.083, //Es
 257.095, //Fm
 258.098, //Md
 259.101, //No
 262.11, //Lr
 261.109, //Rf
 262.114, //Db
 266.122, //Sg
 264.125, //Bh
 269.134, //Hs
 268.139 //Mt
};

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

//LS coefficient for A=atomic weight
const G4double G4AtimaEnergyLossModel::ls_coefficients_a[110][200]=
{	{-0.0286005,-0.0269762,-0.0254384,-0.0239826,-0.0226044,-0.0212998,-0.0200648,-0.0188958,-0.0177891,-0.0167414,-0.0157495,-0.0148105,-0.0139213,-0.0130793,-0.0122818,-0.0115265,-0.0108109,-0.0101329,-0.00949027,-0.00888115,-0.0083036,-0.00775583,-0.00723615,-0.00674295,-0.0062747,-0.00582996,-0.00540738,-0.00500564,-0.00462353,-0.00425989,-0.00391361,-0.00358365,-0.00326903,-0.0029688,-0.00268208,-0.00240803,-0.00214586,-0.00189481,-0.00165416,-0.00142324,-0.0012014,-0.000988038,-0.000782569,-0.000584449,-0.000393155,-0.000208196,-2.91012e-05,0.000144572,0.000313247,0.000477324,0.000637183,0.000793185,0.000945673,0.00109497,0.0012414,0.00138523,0.00152676,0.00166625,0.00180395,0.00194009,0.0020749,0.0022086,0.00234139,0.00247346,0.00260498,0.00273612,0.00286706,0.00299792,0.00312886,0.00325999,0.00339145,0.00352333,0.00365574,0.00378876,0.00392249,0.00405698,0.00419229,0.00432849,0.0044656,0.00460367,0.0047427,0.00488271,0.00502369,0.00516564,0.00530853,0.00545232,0.00559697,0.00574243,0.00588862,0.00603547,0.00618289,0.00633076,0.00647899,0.00662745,0.006776,0.00692451,0.00707282,0.00722077,0.00736819,0.00751491,0.00766074,0.0078055,0.007949,0.00809104,0.00823143,0.00836998,0.00850649,0.00864077,0.00877264,0.0089019,0.0090284,0.00915196,0.00927243,0.00938966,0.00950352,0.00961389,0.00972066,0.00982374,0.00992306,0.0100185,0.0101102,0.0101979,0.0102817,0.0103616,0.0104376,0.0105097,0.010578,0.0106425,0.0107033,0.0107605,0.0108141,0.0108643,0.0109111,0.0109547,0.0109951,0.0110324,0.0110669,0.0110984,0.0111273,0.0111535,0.0111772,0.0111984,0.0112173,0.0112339,0.0112483,0.0112605,0.0112705,0.0112785,0.0112844,0.0112882,0.0112899,0.0112895,0.0112869,0.0112821,0.0112749,0.0112652,0.011253,0.011238,0.01122,0.0111988,0.011174,0.0111455,0.0111127,0.0110753,0.0110328,0.0109847,0.0109303,0.0108689,0.0107998,0.010722,0.0106346,0.0105364,0.0104261,0.0103024,0.0101636,0.0100079,0.00983338,0.00963767,0.00941827,0.0091723,0.0088966,0.00858758,0.00824121,0.00785299,0.00741787,0.0069302,0.00638364,0.00577111,0.00508464,0.00431533,0.00345395,0.00248834,0.00140654,0.000194686,-0.00116268,-0.00268283,-0.00438502,-0.00629005,-0.00842259,-0.0108087},
	{-0.108683,-0.102922,-0.097437,-0.0922162,-0.0872489,-0.0825243,-0.0780321,-0.073762,-0.0697043,-0.0658493,-0.0621879,-0.0587109,-0.0554098,-0.0522762,-0.049302,-0.0464796,-0.0438014,-0.0412604,-0.0388496,-0.0365626,-0.0343929,-0.0323346,-0.0303819,-0.0285294,-0.0267717,-0.0251038,-0.023521,-0.0220186,-0.0205924,-0.0192382,-0.017952,-0.0167301,-0.015569,-0.0144651,-0.0134154,-0.0124167,-0.011466,-0.0105607,-0.00969814,-0.00887572,-0.00809112,-0.00734207,-0.00662644,-0.00594219,-0.00528738,-0.00466019,-0.00405889,-0.00348181,-0.00292739,-0.00239414,-0.00188067,-0.00138562,-0.000907732,-0.000445801,1.31405e-06,0.000434696,0.000855371,0.00126431,0.00166244,0.00205062,0.0024297,0.00280044,0.00316359,0.00351985,0.00386987,0.00421428,0.00455367,0.00488858,0.00521953,0.00554701,0.00587147,0.00619333,0.00651298,0.00683078,0.00714706,0.00746212,0.00777624,0.00808966,0.00840259,0.00871523,0.00902774,0.00934025,0.00965286,0.00996565,0.0102787,0.010592,0.0109055,0.0112192,0.0115331,0.0118471,0.012161,0.0124748,0.0127882,0.013101,0.0134132,0.0137243,0.0140342,0.0143426,0.0146492,0.0149537,0.0152557,0.015555,0.0158511,0.0161438,0.0164326,0.0167172,0.0169973,0.0172725,0.0175424,0.0178067,0.0180651,0.0183173,0.0185629,0.0188017,0.0190335,0.019258,0.019475,0.0196843,0.0198859,0.0200796,0.0202654,0.0204431,0.0206127,0.0207744,0.020928,0.0210737,0.0212116,0.0213417,0.0214643,0.0215794,0.0216873,0.021788,0.0218819,0.0219691,0.0220498,0.0221242,0.0221925,0.022255,0.0223118,0.0223631,0.0224091,0.0224499,0.0224857,0.0225167,0.0225428,0.0225643,0.0225811,0.0225932,0.0226007,0.0226036,0.0226016,0.0225948,0.0225828,0.0225656,0.0225427,0.022514,0.0224789,0.022437,0.0223877,0.0223304,0.0222644,0.0221887,0.0221025,0.0220046,0.0218937,0.0217684,0.0216273,0.0214683,0.0212895,0.0210887,0.0208632,0.0206101,0.0203263,0.020008,0.0196512,0.0192513,0.0188031,0.018301,0.0177384,0.0171081,0.0164021,0.0156115,0.0147258,0.0137341,0.0126235,0.0113801,0.00998803,0.00842986,0.00668603,0.00473508,0.00255242,0.000111379,-0.00261781,-0.0056681,-0.00907593,-0.0128834,-0.0171323,-0.0218726,-0.0271577,-0.0330461},
	{-0.223884,-0.213009,-0.202568,-0.192553,-0.182953,-0.173755,-0.16495,-0.156525,-0.148469,-0.140769,-0.133415,-0.126394,-0.119694,-0.113303,-0.10721,-0.101404,-0.0958714,-0.0906027,-0.0855866,-0.0808123,-0.0762693,-0.0719475,-0.0678369,-0.063928,-0.0602115,-0.0566782,-0.0533196,-0.0501272,-0.0470929,-0.0442089,-0.0414678,-0.0388623,-0.0363856,-0.034031,-0.0317921,-0.029663,-0.0276377,-0.0257108,-0.0238769,-0.0221309,-0.0204681,-0.0188837,-0.0173734,-0.0159331,-0.0145586,-0.0132462,-0.0119923,-0.0107934,-0.00964627,-0.00854773,-0.00749484,-0.00648478,-0.00551487,-0.00458256,-0.00368542,-0.00282117,-0.00198762,-0.0011827,-0.000404448,0.000348997,0.0010794,0.00178843,0.00247768,0.00314864,0.00380272,0.00444127,0.00506554,0.00567674,0.00627597,0.00686428,0.00744268,0.00801208,0.00857334,0.00912727,0.00967462,0.0102161,0.0107522,0.0112837,0.011811,0.0123347,0.012855,0.0133725,0.0138873,0.0143999,0.0149103,0.0154188,0.0159254,0.0164303,0.0169335,0.017435,0.0179346,0.0184323,0.018928,0.0194213,0.0199121,0.0204002,0.0208851,0.0213666,0.0218443,0.0223178,0.0227866,0.0232502,0.0237084,0.0241604,0.024606,0.0250444,0.0254754,0.0258983,0.0263127,0.0267181,0.027114,0.0275001,0.0278758,0.0282409,0.028595,0.0289377,0.0292689,0.0295882,0.0298954,0.0301905,0.0304734,0.0307439,0.0310021,0.031248,0.0314816,0.0317031,0.0319127,0.0321105,0.0322967,0.0324716,0.0326355,0.0327885,0.0329311,0.0330635,0.0331861,0.0332991,0.033403,0.0334979,0.0335842,0.0336623,0.0337323,0.0337945,0.0338491,0.0338964,0.0339365,0.0339694,0.0339954,0.0340144,0.0340265,0.0340315,0.0340294,0.0340199,0.0340028,0.0339778,0.0339445,0.0339023,0.0338507,0.033789,0.0337163,0.0336318,0.0335342,0.0334224,0.0332949,0.03315,0.032986,0.0328007,0.0325918,0.0323567,0.0320922,0.0317951,0.0314616,0.0310874,0.0306677,0.0301973,0.02967,0.0290791,0.0284172,0.0276758,0.0268457,0.025916,0.0248751,0.0237098,0.0224056,0.0209459,0.0193125,0.0174852,0.0154416,0.0131562,0.0106012,0.00774588,0.00455597,0.000993742,-0.00298393,-0.00742085,-0.0123683,-0.0178814,-0.0240203,-0.030853,-0.0384474,-0.0468817},
	{-0.356328,-0.340686,-0.325539,-0.310886,-0.296723,-0.283047,-0.269853,-0.257134,-0.244884,-0.233095,-0.221759,-0.210866,-0.200406,-0.19037,-0.180747,-0.171526,-0.162694,-0.154242,-0.146157,-0.138426,-0.131039,-0.123984,-0.117247,-0.110818,-0.104685,-0.0988357,-0.0932592,-0.0879442,-0.0828796,-0.0780547,-0.073459,-0.0690823,-0.0649147,-0.0609465,-0.0571684,-0.0535713,-0.0501465,-0.0468855,-0.0437803,-0.040823,-0.0380061,-0.0353223,-0.0327648,-0.0303268,-0.0280019,-0.0257842,-0.0236676,-0.0216467,-0.0197161,-0.0178706,-0.0161054,-0.0144159,-0.0127976,-0.0112463,-0.00975795,-0.00832875,-0.00695503,-0.00563334,-0.00436036,-0.00313296,-0.00194816,-0.000803139,0.000304789,0.00137817,0.00241941,0.00343079,0.00441446,0.00537247,0.00630674,0.00721908,0.0081112,0.00898469,0.00984106,0.0106817,0.011508,0.012321,0.013122,0.013912,0.0146919,0.0154626,0.0162249,0.0169795,0.017727,0.018468,0.019203,0.0199323,0.0206563,0.0213752,0.0220892,0.0227985,0.023503,0.0242028,0.0248977,0.0255876,0.0262723,0.0269516,0.027625,0.0282923,0.028953,0.0296067,0.0302529,0.030891,0.0315205,0.0321408,0.0327514,0.0333515,0.0339407,0.0345182,0.0350836,0.0356361,0.0361754,0.0367007,0.0372117,0.0377078,0.0381886,0.0386538,0.039103,0.0395359,0.0399523,0.0403521,0.0407351,0.0411013,0.0414507,0.0417834,0.0420995,0.0423992,0.0426827,0.0429502,0.0432021,0.0434387,0.0436603,0.0438675,0.0440605,0.0442399,0.0444061,0.0445595,0.0447005,0.0448297,0.0449474,0.045054,0.0451499,0.0452355,0.0453111,0.045377,0.0454334,0.0454806,0.0455186,0.0455475,0.0455675,0.0455784,0.0455801,0.0455724,0.0455552,0.0455279,0.0454901,0.0454413,0.0453806,0.0453074,0.0452206,0.0451191,0.0450015,0.0448663,0.0447118,0.0445361,0.0443368,0.0441115,0.0438573,0.0435709,0.0432487,0.0428867,0.0424802,0.042024,0.0415125,0.040939,0.0402963,0.0395763,0.0387698,0.0378668,0.0368557,0.0357238,0.034457,0.0330394,0.0314533,0.0296791,0.027695,0.0254765,0.0229968,0.0202258,0.0171305,0.0136742,0.00981578,0.00551186,0.000713059,-0.00463419,-0.0105884,-0.0172145,-0.0245801,-0.0327606,-0.0418365,-0.0518915},
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};

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

//LS coefficient for A=atomic weight * 1.05
const G4double G4AtimaEnergyLossModel::ls_coefficients_ahi[110][200]=
{
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	{-3.4045,-3.3752,-3.34588,-3.31653,-3.28716,-3.25776,-3.22834,-3.19888,-3.1694,-3.13989,-3.11034,-3.08075,-3.05113,-3.02146,-2.99176,-2.96201,-2.93221,-2.90236,-2.87246,-2.84251,-2.8125,-2.78242,-2.75228,-2.72207,-2.69178,-2.66142,-2.63098,-2.60046,-2.56984,-2.53913,-2.50832,-2.4774,-2.44637,-2.41522,-2.38395,-2.35255,-2.32101,-2.28933,-2.2575,-2.2255,-2.19334,-2.161,-2.12848,-2.09576,-2.06283,-2.0297,-1.99633,-1.96273,-1.92888,-1.89478,-1.8604,-1.82574,-1.79078,-1.75551,-1.71992,-1.68399,-1.64771,-1.61107,-1.57404,-1.53663,-1.4988,-1.46055,-1.42186,-1.38273,-1.34312,-1.30303,-1.26246,-1.22137,-1.17977,-1.13763,-1.09495,-1.05173,-1.00794,-0.963594,-0.918673,-0.873177,-0.827106,-0.78046,-0.733241,-0.685456,-0.637111,-0.58822,-0.538794,-0.488854,-0.438418,-0.387512,-0.336165,-0.284409,-0.232281,-0.17982,-0.127072,-0.074084,-0.02091,0.0323938,0.0857674,0.139147,0.192465,0.245652,0.298634,0.351337,0.403684,0.455597,0.506996,0.557802,0.607936,0.657319,0.705874,0.753527,0.800204,0.845837,0.890358,0.933707,0.975826,1.01666,1.05617,1.0943,1.13102,1.1663,1.20012,1.23246,1.26329,1.29262,1.32044,1.34675,1.37157,1.3949,1.41676,1.43716,1.45614,1.47372,1.48992,1.50478,1.51833,1.5306,1.54162,1.55143,1.56005,1.56753,1.57389,1.57915,1.58336,1.58653,1.58868,1.58984,1.59002,1.58925,1.58752,1.58484,1.58123,1.57668,1.57119,1.56475,1.55736,1.549,1.53964,1.52928,1.51789,1.50543,1.49188,1.4772,1.46136,1.4443,1.426,1.40641,1.38547,1.36314,1.33936,1.3141,1.28729,1.25889,1.22885,1.19713,1.16368,1.12848,1.09149,1.0527,1.01209,0.969659,0.925425,0.87941,0.831651,0.782201,0.731129,0.678519,0.624464,0.569074,0.512468,0.454771,0.39611,0.336611,0.2764,0.215585,0.154267,0.0925296,0.0304376,-0.0319538,-0.0946098,-0.1575,-0.220604,-0.283896}
};

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
   
const G4double G4AtimaEnergyLossModel::ionisation_potentials_z[121] = {
    9999999,  // 0   
    19.2, // H
    41.8, // He
    40.0,
    63.7,
    76.0,
    78.0, // C
    82.0,
    95.0,
    115.0,
    137.0,
    149.0,
    156.0,
    166.0,
    173.0,
    173.0,
    180.0,
    174.0,
    188.0,
    190.0,
    191.0, //Ca (20)
    216.0,
    233.0,
    245.0,
    257.0,
    272.0,
    286.0, //Fe 26
    297.0,
    311.0,
    322.0,
    330.0,
    334.0,
    350.0,
    347.0,
    348.0,
    343.0,
    352.0,
    363.0,
    366.0,
    379.0,
    393.0,
    417.0,
    424.0,
    428.0,
    441.0,
    449.0,
    470.0,
    470.0,
    469.0,
    488.0,
    488.0, //Sn 50
    487.0,
    485.0,
    491.0,
    482.0, // Xe 54
    488.0,
    491.0,
    501.0,
    523.0,
    535.0,
    546.0,
    560.0,
    574.0,
    580.0,
    591.0,
    614.0,
    628.0,
    650.0,
    658.0,
    674.0,
    684.0,
    694.0,
    705.0,
    718.0,
    727.0,
    736.0,
    746.0,
    757.0,
    790.0,
    790.0, // Au 79
    800.0,
    810.0,
    823.0, //Pb 82
    823.0,
    830.0,
    825.0,
    794.0,
    827.0,
    826.0,
    841.0,
    847.0,
    878.0,
    890.0, // U 92
      900.0,
      910.0,
      920.0,
      930.0,
      940.0,
      950.0,
      960.0,
     970.0,
     980.0,
     990.0,
    1000.0,
    1010.0,
    1020.0,
    1030.0,
    1040.0,
    1050.0,
    1060.0,
    1070.0,
    1080.0,
    1090.0,
    1100.0,
    1110.0,
    1120.0,
    1130.0,
    1140.0,
    1150.0,
    1160.0,
    1170.0,
    };

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

const G4double G4AtimaEnergyLossModel::x0[92]= {
1.8639, 2.2017,  0.1304, 0.0592, 0.0305, -.0178, 1.7378, 1.7541, 1.8433, 2.0735,
0.2880, 0.1499,  0.1708, 0.2014, 0.1696, 0.1580, 1.5555, 1.7635, 0.3851, 0.3228,
0.1640, 0.0957,  0.0691, 0.0340, 0.0447, -.0012, -.0187, -.0566, -.0254, 0.0049,
0.2267, 0.3376,  0.1767, 0.2258, 1.5262, 1.7158, 0.5737, 0.4585, 0.3608, 0.2957,
0.1785, 0.2267,  0.0949, 0.0599, 0.0576, 0.0563, 0.0657, 0.1281, 0.2406, 0.2879,
0.3189, 0.3296,  0.0549, 1.5630, 0.5473, 0.4190, 0.3161, 0.2713, 0.2333, 0.1984,
0.1627, 0.1520,  0.1888, 0.1058, 0.0947, 0.0822, 0.0761, 0.0648, 0.0812, 0.1199,
0.1560, 0.1965,  0.2117, 0.2167, 0.0559, 0.0891, 0.0819, 0.1484, 0.2021, 0.2756,
0.3491, 0.3776,  0.4152, 0.4267, 0.4300, 1.5368, 0.6000, 0.5991, 0.4559, 0.4202,
0.3144, 0.2260 };

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

const G4double G4AtimaEnergyLossModel::x1[92]= {
3.2718, 3.6122,  1.6397, 1.6922, 1.9688, 2.3415, 4.1323, 4.3213, 4.4096, 4.6421,
3.1962, 3.0668,  3.0127, 2.8715, 2.7815, 2.7159, 4.2994, 4.4855, 3.1724, 3.1191,
3.0593, 3.0386,  3.0322, 3.0451, 3.1074, 3.1531, 3.1790, 3.1851, 3.2792, 3.3668,
3.5434, 3.6096,  3.5702, 3.6264, 4.9899, 5.0748, 3.7995, 3.6778, 3.5542, 3.4890,
3.2201, 3.2784,  3.1253, 3.0834, 3.1069, 3.0555, 3.1074, 3.1667, 3.2032, 3.2959,
3.3489, 3.4418,  3.2596, 4.7371, 3.5914, 3.4547, 3.3293, 3.3432, 3.2773, 3.3063,
3.3199, 3.3460,  3.4633, 3.3932, 3.4224, 3.4474, 3.4782, 3.4922, 3.5085, 3.6246,
3.5218, 3.4337,  3.4805, 3.4960, 3.4845, 3.5414, 3.5480, 3.6212, 3.6979, 3.7275,
3.8044, 3.8073,  3.8248, 3.8293, 4.0000, 4.9889, 4.0000, 3.9428, 3.7966, 3.7681,
3.5079, 3.3721 };

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

const G4double G4AtimaEnergyLossModel::afermi[92]= {
 0.14092, 0.13443,  0.95136, 0.80392, 0.56224, 0.26142, 0.15349, 0.11778, 0.11083, .08064,
 0.07772, 0.08163,  0.08024, 0.14921, 0.23610, 0.33992, 0.19849, 0.19714, 0.19827, .15643,
 0.15754, 0.15662,  0.15436, 0.15419, 0.14973, 0.14680, 0.14474, 0.16496, 0.14339, .14714,
 0.09440, 0.07188,  0.06633, 0.06568, 0.06335, 0.07446, 0.07261, 0.07165, 0.07138, .07177,
 0.13883, 0.10525,  0.16572, 0.19342, 0.19205, 0.24178, 0.24585, 0.24609, 0.23879, .18689,
 0.16652, 0.13815,  0.23766, 0.23314, 0.18233, 0.18268, 0.18591, 0.18885, 0.23265, .23530,
 0.24280, 0.24698,  0.24448, 0.25109, 0.24453, 0.24665, 0.24638, 0.24823, 0.24889, .25295,
 0.24033, 0.22918,  0.17798, 0.15509, 0.15184, 0.12751, 0.12690, 0.11128, 0.09756, .11014,
 0.09455, 0.09359,  0.09410, 0.09282, 0.09000, 0.20798, 0.08000, 0.08804, 0.08567, 0.08655,
 0.14770,  0.19677 };

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

const G4double G4AtimaEnergyLossModel::c[92]= {
9.5835, 11.1393, 3.1221, 2.7847, 2.8477, 2.8680, 10.5400, 10.7004, 10.9653, 11.9041,
5.0526, 4.5297,  4.2395, 4.4351, 4.5214, 4.6659, 11.1421, 11.9480, 5.6423, 5.0396,
4.6949, 4.4450,  4.2659, 4.1781, 4.2702, 4.2911, 4.2601, 4.3115, 4.4190, 4.6906,
4.9353, 5.1411,  5.0510, 5.3210, 11.7307,12.5115,6.4776, 5.9867, 5.4801 , 5.1774,
5.0141, 4.8793,  4.7769, 4.7694, 4.8008, 4.9358, 5.0630, 5.2727, 5.5211, 5.5340,
5.6241, 5.7131,  5.9488, 12.7281, 6.9135, 6.3153, 5.7850, 5.7837, 5.8096, 5.8290,
5.8224, 5.8597,  6.2278, 5.8738, 5.9045, 5.9183, 5.9587, 5.9521, 5.9677, 6.3325,
5.9785, 5.7139,  5.5262, 5.4059, 5.3445, 5.3083, 5.3418, 5.4732, 5.5747, 5.9605,
6.1365, 6.2018,  6.3505, 6.4003, 6.4, 13.2839, 7., 7.0452, 6.3742, 6.2473,
6.0327, 5.8694 };

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

const G4double G4AtimaEnergyLossModel::m0[92]= {
5.7273, 5.8347,  2.4993, 2.4339, 2.4512, 2.8697, 3.2125, 3.2913, 3.2962, 3.5771,
3.6452, 3.6166,  3.6345, 3.2546, 2.9158, 2.6456, 2.9702, 2.9618, 2.9233, 3.0745,
3.0517, 3.0302,  3.0163, 2.9896, 2.9796, 2.9632, 2.9502, 2.8430, 2.9044, 2.8652,
3.1314, 3.3306,  3.4176, 3.4317, 3.4670, 3.4051, 3.4177, 3.4435, 3.4585, 3.4533,
3.0930, 3.2549,  2.9738, 2.8707, 2.8633, 2.7239, 2.6899, 2.6772, 2.7144, 2.8576,
2.9319, 3.0354,  2.7276, 2.7414, 2.8866, 2.8906, 2.8828, 2.8592, 2.7331, 2.7050,
2.6674, 2.6403,  2.6245, 2.5977, 2.6056, 2.5849, 2.5726, 2.5573, 2.5469, 2.5141,
2.5643, 2.6155,  2.7623, 2.8447, 2.8627, 2.9608, 2.9658, 3.0417, 3.1101, 3.0519,
3.1450, 3.1608,  3.1671, 3.1830, 1.1111, 2.7409, 1.1111, 3.2454, 3.2683, 3.2610,
2.9845, 2.8171 };

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......

const G4double G4AtimaEnergyLossModel::del_0[92]= {
0.0,  0.00,  0.14, 0.14, 0.14, 0.12, 0.00, 0.00, 0.00, 0.00,
0.08, 0.08,  0.12, 0.14, 0.14, 0.14, 0.00, 0.00, 0.10, 0.14,
0.10, 0.12,  0.14, 0.14, 0.14, 0.12, 0.12, 0.10, 0.08, 0.08,
0.14, 0.14,  0.08, 0.10, 0.00, 0.00, 0.14, 0.14, 0.14, 0.14,
0.14, 0.14,  0.14, 0.14, 0.14, 0.14, 0.14, 0.14, 0.14, 0.14,
0.14, 0.14,  0.00, 0.00, 0.14, 0.14, 0.14, 0.14, 0.14, 0.14,
0.14, 0.14,  0.14, 0.14, 0.14, 0.14, 0.14, 0.14, 0.14, 0.14,
0.14, 0.14,  0.14, 0.14, 0.08, 0.10, 0.10, 0.12, 0.14, 0.14,
0.14, 0.14,  0.14, 0.14, 0.00, 0.00, 0.00, 0.14, 0.14, 0.14,
0.14, 0.14 };

//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
